Constrained integrated inventory model for multi-item under mixture of distributions

Department of Mathematics, The Gandhigram Rural Institute – Deemed University, Gandhigram 624 302, Tamil Nadu, India.

^* Corresponding author: ganeshkumarnov23@gmail.com

Received: 13 April 2017
Accepted: 21 December 2017

Abstract

When the demand of different customers are not identical during the lead time, then one cannot use only a single distribution to describe the demand during that lead time. Hence, in this paper we have studied a mixture of normal distributions and a mixture of distribution free for several products under vendor-buyer integrated approach (coordination between both parties). Many integrated inventory models have proved that the integrated total cost is minimum when compared to sum of the total cost of the individuals. The inventory is continuously reviewed by the buyer and next order is placed when the inventory reaches some level called reorder level. The buyer has limited warehouse space capacity and also limited budget to purchase all products. The lead time of receiving all products from the vendor is a variable which is controlled by adding crashing cost. Shortages are allowed for all products and a fraction of shortages will be backordered and the remaining are lost. A mathematical model is developed and a solution procedure is employed in this study to obtain optimum order quantities, lead time and number of shipments in which the integrated total cost function attains its minimum subject to the floor space constraint and budget constraint. The expected integrated cost function is non-linear mixed integer with inequality constraints. Therefore, the proposed model have been solved by using Lagrangian multiplier technique. Finally numerical examples and sensitivity analysis were performed to illustrate the effectiveness of the proposed model.